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A new algorithm for lossless compression of hyperspectral imagery is proposed. First, the average value of four neighbour pixels of the current pixel is calculated as local mean, which is subtracted by the current pixel to eliminate correlation in the current band image. The residual produced by this step is called local difference. The local differences of the pixels which co-locate with the current pixel in previous bands form the input vector of the recursive least square (RLS) filter, by which the prediction value of the current local difference is produced. Then, the prediction residual is sent to the adaptive arithmetic encoder. Experiment results show that the proposed algorithm produces state-of-the-art performance with relatively low complexity, and it is suitable for real-time compression on satellites.